An averaged-field approach for obtaining the band structure of a dielectric photonic crystal

An averaged-field approach is suggested for obtaining the explicit form of the dispersion equation for electromagnetic waves propagating in a three- or two-dimensional dielectric photonic crystal when the dimension of the inclusions is small compared with the longest period of the rectangular lattice of the photonic crystal. The band structure is obtained in an explicit and simple way. The method is verified numerically by comparing with the conventional plane-wave expansion method for a special case.

[1]  H. Kogelnik,et al.  Coupled‐Wave Theory of Distributed Feedback Lasers , 1972 .

[2]  R. Collin.  Foundations for microwave engineering , 1966 .

[3]  Genack,et al.  Suppression of molecular interactions in periodic dielectric structures. , 1988, Physical review letters.

[4]  D. M. Atkin,et al.  All-silica single-mode optical fiber with photonic crystal cladding. , 1996, Optics letters.

[5]  T. Gmitter,et al.  Inhibited and enhanced spontaneous emission from optically thin AlGaAs/GaAs double heterostructures. , 1988, Physical review letters.

[6]  A. Maradudin,et al.  Photonic band structure of two-dimensional systems: The triangular lattice. , 1991, Physical review. B, Condensed matter.

[7]  J. Joannopoulos,et al.  Photonic crystals: putting a new twist on light , 1997, Nature.

[8]  Zhang,et al.  Theory of photon bands in three-dimensional periodic dielectric structures. , 1990, Physical review letters.

[9]  Chin,et al.  Green's function and lattice sums for electromagnetic scattering by a square array of cylinders. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  Ross C. McPhedran,et al.  Lattice Sums for an Electromagnetic Scattering Problem , 1992 .

[11]  John,et al.  Strong localization of photons in certain disordered dielectric superlattices. , 1987, Physical review letters.

[12]  Steven G. Johnson,et al.  Photonic Crystals: Molding the Flow of Light , 1995 .

[13]  Maradudin,et al.  Photonic band structures of two-dimensional systems containing metallic components. , 1994, Physical review. B, Condensed matter.

[14]  R. Collin.  Field theory of guided waves , 1960 .

[15]  H A Haus,et al.  Photonic bands: Convergence problems with the plane-wave method. , 1992, Physical review. B, Condensed matter.

[16]  Chan,et al.  Existence of a photonic gap in periodic dielectric structures. , 1990, Physical review letters.

[17]  E. Yablonovitch,et al.  Inhibited spontaneous emission in solid-state physics and electronics. , 1987, Physical review letters.

[18]  Leung,et al.  Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media. , 1990, Physical review letters.